(The idea for this project is due to Matt Richey, St. Olaf College. He developed the problem on which this project is based.)
Most cassette tape decks and VCRs have a counter which changes as the deck operates. However, most people are unaware of the relationship between the value of the counter and the time that the tape has been playing (the elapsed time). The purpose of this project is to investigate this relationship.
For this project, you will need an older model VCR or a tape deck which has a counter, and a watch or clock. You need to use a VCR or tape player which has a counter rather than a timer. If no one in your group has a VCR or tape deck with a counter, I have a tape player/recorder that you can borrow. It is important to collect sufficient data so that you have a good model for this situation. You should collect at least 40 minutes of data (and more data would be better). If you do not have sufficient data, you may not get a very good model.
Collect data and derive a formula expressing elapsed time, t, as a function of the counter reading, x. That is, determine a function f so that t = f(x) provides a reasonable fit to the collected data. You will need to give considerable attention as to how to measure the goodness of the fit. In the Model Interpretation section of your paper, discuss how good your model is, that is, how well your model fits your data.
Collect your data and develop the model as a group. Each group is to turn in one group report on this project.
Follow the Project Report Format given in the first project assignment. You may want to look at some of the winning papers from the Mathematical Modeling Contest which are published in the Fall issue of the UMAP Journal for some general examples of the style for your paper.